scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

Generation of analytic semigroups in theL p topology by elliptic operators inR n

1988 ◽  
Vol 61 (3) ◽  
pp. 235-255 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Elliptic Operators ◽  
Analytic Semigroups

Time-dependent Nonlinear Perturbations of Analytic Semigroups

2007 ◽  
pp. 457-502
Author(s):  
Robert H. Martin ◽  
Toshitaka Matsumoto ◽  
Shinnosuke Oharu ◽  
Naoki Tanaka
Keyword(s):  
Time Dependent ◽  
Analytic Semigroups ◽  
Nonlinear Perturbations

Relatively Bounded Rank One Perturbations of Non-Analytic Semigroups Can Generate Large Point Spectrum

2007 ◽  
Vol 75 (2) ◽  
pp. 470-476 ◽  
Author(s):  
Wolfgang Desch ◽  
Gudrun Schappacher ◽  
Wilhelm Schappacher
Keyword(s):  
Point Spectrum ◽  
Analytic Semigroups ◽  
Rank One ◽  
Bounded Rank

scholarly journals Analytic Semigroups of Holomorphic Mappings and Composition Operators

2017 ◽  
Vol 18 (2) ◽  
pp. 269-294 ◽  
Author(s):  
Mark Elin ◽  
David Shoikhet ◽  
Nikolai Tarkhanov
Keyword(s):  
Composition Operators ◽  
Holomorphic Mappings ◽  
Analytic Semigroups
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